Engineering Board Exam Reviewer · Derivatives of Algebraic Functions · hard

Find the derivative of y=x3/x2+1.

1. x4+3x2/(x2+1)2
2. x2/x2+1
3. 3x2/(x2+1)2
4. x4+3x2/x2+1

Answer

A. x4+3x2/(x2+1)2

Solution

By the quotient rule: y'=3x2(x2+1)-x3(2x)/(x2+1)2=x4+3x2/(x2+1)2.

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